Database System Concepts
Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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![画像:**Simplifying Boolean Expressions** **Problem 1:** Simplify the following Boolean expression to a minimum number of literals: \[ x'y'z' + x'yz + xy'z + xyz' + xyz \] The aim is to reduce the expression to three literals. **Steps for Simplification:** 1. **Identify Common Terms:** - Look for common variables in the terms to factor out and simplify the expression. 2. **Apply Boolean Algebra Rules:** - Use rules such as the Consensus Theorem, Distribution, and Absorption laws. 3. **Combine Terms:** - Simplify by combining like terms or eliminating redundant terms. The goal is to express the function with the fewest possible variables.](https://content.bartleby.com/qna-images/question/65f3802d-af3c-471a-8521-227491fd8d12/65430b0c-6303-4439-816d-aad631489eaf/cmmeji_thumbnail.jpeg){kind=link}
Transcribed Image Text:**Simplifying Boolean Expressions**
**Problem 1:**
Simplify the following Boolean expression to a minimum number of literals:
\[ x'y'z' + x'yz + xy'z + xyz' + xyz \]
The aim is to reduce the expression to three literals.
**Steps for Simplification:**
1. **Identify Common Terms:**
- Look for common variables in the terms to factor out and simplify the expression.
2. **Apply Boolean Algebra Rules:**
- Use rules such as the Consensus Theorem, Distribution, and Absorption laws.
3. **Combine Terms:**
- Simplify by combining like terms or eliminating redundant terms.
The goal is to express the function with the fewest possible variables.
Expert Solution
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Step 1: Introducing Boolean Expression
A Boolean expression is a mathematical and logical construct that uses binary variables and logical operations. The variable in a Boolean expression can take only two values: true or false, often represented as 1 or 0 respectively.
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